Solving Systems: Introduction to Linear Combinations Answers

Two systems of equations are shown. The first equation in system B is the original equation in system A. The second equation in system B is the sum of that equation and a multiple of the second equation in system A.

What is the solution to this system of linear equations?2x + y = 13x – y = –6

The solution to the system of equation below is (−2, −1).2x − 3y = −1 11x − 9y = −13When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.

Mira picked two numbers from a bowl. The difference of the two numbers was 4, and the sum of one-half of each number was 18. The system that represents Mira’s numbers is below. x – y = 4x + y = 18Which two numbers did Mira pick?

What is the solution to this system of linear equations?x − 3y = −2x + 3y = 16

What is the solution to this system of linear equations?y − x = 6y + x = −10

What is the solution to this system of linear equations?2x + 3y = 37x – 3y = 24

Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.x + y = 3,500x – y = 2,342Solve the system of equations. How many contemporary titles does Jarred have?

What is the x-value in the solution to this system of linear equations?2x − y = 11x + 3y = −5

A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown.12x + 12y=1564x + 6y=62